Pulsed field gradient NMR diffusion measurement in nanoporous materials

Abstract

Labeling in diffusion measurements by pulsed field gradient (PFG) NMR is based on the observation of the phase of nuclear spins acquired in a constant magnetic field with purposefully superimposed field gradients. This labeling does in no way affect microdynamics and provides information about the probability distribution of molecular displacements as a function of time. An introduction of the measuring principle is followed by a detailed description of the ranges of measurements and their limitation. Particular emphasis is given to an explanation of possible pitfalls in the measurements and the ways to circumvent them. Showcases presented for illustrating the wealth of information provided by PFG NMR include a survey on the various patterns of concentration dependence of intra-particle diffusion and examples of transport inhibition by additional transport resistances within the nanoporous particles and on their external surface. The latter information is attained by combination with the outcome of tracer exchange experiments, which are shown to become possible via a special formalism of PFG NMR data analysis. Further evidence provided by PFG NMR concerns diffusion enhancement in pore hierarchies, diffusion anisotropy and the impact of diffusion on chemical conversion in porous catalysts. A compilation of the specifics of PFG NMR and of the parallels with other measurement techniques concludes the paper.

Single-molecule observation of diffusion and catalysis in nanoporous solids

“…The obtained diffusion constant was similar to that of similarly-sized vacuum gas oil feedstock molecules measured with adsorption experiments [56]. Intraparticle diffusion has been found to be the limiting factor in the conversion at operating conditions [96,97], which is discussed in detail by Kärger et al in their PFG NMR-themed contribution in this issue [10]. Indeed, the Thiele modulus was approximated for the cracking of cetane (C 16 ) to octane (C 8 ) and was in line with previously reported values, validating the single-molecule approach to study mass transport in these systems [56].…”

“…Nanoporous solids are omnipresent in adsorption, molecular separation, and catalytic conversion technologies [1][2][3][4][5][6][7], and diffusion of guest molecules in these functional materials is among the rate-limiting processes in their technological application. The economic feasibility of these technologies often depends on the diffusivity of the guest molecules, therefore understanding of the underlying processes is not only of fundamental, but also of industrial and societal importance [8][9][10][11]. However, as the pore size of nanoporous solids is comparable to the size of the diffusant, a theoretical framework explaining this diffusion is particularly complex.…”

“…However, as the pore size of nanoporous solids is comparable to the size of the diffusant, a theoretical framework explaining this diffusion is particularly complex. Frequent interactions between guest (molecule) and host (nanoporous solid) strongly affect diffusion and adsorption behavior giving rise to complex heterogeneous motion [8][9][10][11]. Investigations at the single-molecule level can reveal these heterogeneities and thus provide deeper insight into such guest-host interactions and their effect on mass transport [4,[12][13][14][15][16][17].…”

Diffusion in Nanoporous Solids in the Focus of IUPAC – A Tribute to Jens Weitkamp

“…Their spatial resolution is, correspondingly, in the range of micrometers as a typical size of nanoporous crystals. Their most prominent representative is the pulsed field gradient (PFG) NMR technique [88,89]. Its key information, the probability distribution of molecular displacements during an observation time of milliseconds to seconds, is based on the observation of incredibly large molecular ensembles (on the order of 10 10 ), in contrast to single-molecule tracking (SMT [90]), by which one is able to trace diffusion paths of the individual molecules.…”

Diffusion and reaction in pore hierarchies by the two-region model

“…Such a possibility is provided within the frame of the so-called two-region model of diffusion. Originally introduced for quantifying PFG NMR diffusion measurements (see [3,40] in this Thematic Issue) in beds of zeolite crystallites [37,38,43], it has meanwhile found widespread application in compartmented systems quite in general [1,5,71,90]. This refers, in particular, to its application to diffusion studies with assemblages of cells in organic tissues [27,66,93], where the term "Kärger model" [22,70,92] has been coined for this approach.…”